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Weighing Problem Resurected


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#1 Prime

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Posted 23 February 2013 - 02:05 AM

You have a dozen (12) stones weighing a whole number of grams between 1 and 6 each. You can obtain one reference weight of your choosing.

What reference weight can you choose to be able to figure out the individual weights of the 12 stones using a balance device for any possibility that may exist therein?

 

For an encore: what is the maximum weight range of stones (1 to N) that you could solve using 2 reference weights of your choice? Provided you can have as many  stones as you need.

I don't believe, I have solved this one myself. We could make it a community project after the first question is answered.
 

HISTORICAL NOTE:

This problem originated on Brain Den. I constructed it based on Bonanova's problem Weighty  Thoughts: http://brainden.com/...4932--/?p=84107 few years ago.

Back then limited number of people participated. The solution found was for specific numbers in that problem (range 1 to 5) – not general. I'd like to give it another try.


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Past prime, actually.


#2 ThunderCloud

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Posted 23 February 2013 - 02:25 AM

I thought I had this one... but found a flaw in my reasoning. [solution withdrawn] :blush:


Edited by ThunderCloud, 23 February 2013 - 02:33 AM.

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#3 CaptainEd

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Posted 23 February 2013 - 03:27 AM

First part: do we know that all weights between 1-6 are represented in the 12 stones? Or is it possible that we have, say, 12 stones each waiting 6?
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#4 phil1882

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Posted 23 February 2013 - 03:29 AM

Spoiler for

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#5 ThunderCloud

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Posted 23 February 2013 - 03:38 AM

You have a dozen (12) stones weighing a whole number of grams between 1 and 6 each. You can obtain one reference weight of your choosing.

What reference weight can you choose to be able to figure out the individual weights of the 12 stones using a balance device for any possibility that may exist therein?

 

For an encore: what is the maximum weight range of stones (1 to N) that you could solve using 2 reference weights of your choice? Provided you can have as many  stones as you need.

I don't believe, I have solved this one myself. We could make it a community project after the first question is answered.
 

HISTORICAL NOTE:

This problem originated on Brain Den. I constructed it based on Bonanova's problem Weighty  Thoughts: http://brainden.com/...4932--/?p=84107 few years ago.

Back then limited number of people participated. The solution found was for specific numbers in that problem (range 1 to 5) – not general. I'd like to give it another try.

Spoiler for One method, though a bit of a cheat...


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#6 Prime

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Posted 23 February 2013 - 03:45 AM

First part: do we know that all weights between 1-6 are represented in the 12 stones? Or is it possible that we have, say, 12 stones each waiting 6?

There is no guaranty what weights are present/absent in your collection. The only guaranty is that each of the stones weighs a whole number of grams between 1 and 6.

12 stones each weighing 6 grams is one of the variations we must account for.


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Past prime, actually.


#7 CaptainEd

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Posted 23 February 2013 - 04:25 AM

I like T-cloud's cheat. It's not a reference weight, but just a found object that represents a difference. Good outside the box thinking!
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#8 CaptainEd

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Posted 23 February 2013 - 04:32 AM

Part 2: you can have as many stones as you want. Which stones? Reference stones of my two chosen denominations? Or as many unknown stones?
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#9 CaptainEd

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Posted 23 February 2013 - 04:36 AM

Part 2: you can have as many stones as you want. Which stones? Reference stones of my two chosen denominations? Or unknown stones?
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#10 Prime

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Posted 23 February 2013 - 04:42 AM

Part 2: you can have as many stones as you want. Which stones? Reference stones of my two chosen denominations? Or as many unknown stones?

For the part 2, you can have 2 reference weights of your choice, as many stones as you want in the weight range from 1 to N. (Must find the largest N and the 2 reference weights.)

Let's solve the first part first. No tricks, no cheating, no different interpretations of the OP. If there is an ambiguity, I'll clarify it.


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Past prime, actually.





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